It is known that deep (convolutional) neural networks are of great importance in image recognition [1]}, [2]}. In [3]}, it was found through controlled experiments that the increase of depth in networks actually improves its performance and accuracy, in exchange, of course, for additional time complexity. However, in the case that the depth is overly increased, the accuracy might get stagnant or even degraded [3]}. In addition, considering deeper networks may impede the learning process which is due to the vanishing or exploding of the gradient [5]}, [6]}. Apparently, deeper neural networks are more difficult to train. To address such an issue, the authors in [7]} recommended the used of residual learning to facilitate the training of networks that are considerably deeper than those used previously. Such networks are referred to as residual network or ResNet. Let \(n\)  and \(m\)  be the dimensions of the input and output data. Let \(N\)  be the number of nodes of each layers. A ResNet can be represented as
\(\left\lbrace \begin{aligned}x^{(l+1)} &= x^{(l)}+f^{(l)}(x^{(l)}), & l=0,1,\ldots ,L-1, \\x^{(0)} &= Q\xi . &\end{aligned}\right.\) 
